Elliptic curve isogeny class 4.1-b over number field \(\Q(\sqrt{273}) \)

• Base field: \(\Q(\sqrt{273}) \)
• Label: 2.2.273.1-4.1-b
• Conductor: 4.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{273}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 68 \); class number \(2\).

Elliptic curves in class 4.1-b over \(\Q(\sqrt{273}) \)

Isogeny class 4.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
4.1-b1	\( \bigl[a\) , \( -1\) , \( a\) , \( 30943198 a - 271104296\) , \( 322779565859 a - 2827986628012\bigr] \)
4.1-b2	\( \bigl[a\) , \( a\) , \( a\) , \( 153 a - 1119\) , \( 2945 a - 25018\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph